Authorities in Los Angeles have offered a $1m (£633,000) reward for information about the rogue ex-police officer suspected of killing three people after a huge manhunt failed to catch him.

Mayors, police chiefs and federal officials announced the bounty at a joint press conference as the trail for Christopher Dorner in the Big Bear ski resort area went cold.

"We will not tolerate this reign of terror that has robbed us of the peace of mind that the residents of southern California deserve," said the mayor of Los Angeles, Antonio Villaraigosa, announcing what was thought to be the biggest reward in state history.

Police unions, government agencies and private donors contributed to the fund, he said, to "bring this tragedy to an end". He urged the public not to engage a fugitive deemed armed and extremely dangerous.

The show of official unity and the unusually large reward underlined anxiety that a dragnet of helicopters and swat teams in Big Bear, a snowy mountain resort north of LA, had failed to net Dorner.

The former navy reservist and trained marksman has declared war on officers and their families in revenge for being sacked from the police. His rampage and the LAPD's blundering response – shooting and wounding innocent people – has transfixed the US and turned Dorner, in some quarters, into a folk hero.

Charlie Beck, the LAPD chief, told a news conference Dorner was engaging in "domestic terrorism" that could not go unanswered: "This is not about capturing a fleeing fugitive, this is about preventing a future crime. Every day that Dorner is loose … [an] attack on a police officer, or family is likely. We ask the public to help us find Dorner before he kills again." Beck said that 50 police officers and their families thought to be on a hit list were under protection.

On Saturday, in a separate development, the police chief ordered a review of the disciplinary case that led to Dorner's dismissal and promised to talk with him if he surrendered. "I do this not to appease a murderer. I do it to reassure the public that their police department is transparent and fair."

In an online manifesto posted before his shooting spree, Dorner alleged that racist colleagues had drummed him out for protesting about a training partner's assault on a homeless man in 2007. An investigation in 2009 found that there was no assault and Dorner had lied.

A joint taskforce involving the LAPD, FBI and other police forces will examine a case that Beck acknowledged had revived concerns about racism within his force. "I feel we need to … publicly address Dorner's allegations regarding his termination of employment," he said.

Police hoped to corner Dorner at Big Bear after his truck was found abandoned, on fire on a back road. Its axle was damaged and weapons and survival gear were inside. Swat teams deployed, battling poor visibility, but after five days there was no sign of the fugitive. Some teams have pulled out, leaving about 50 officers still scouring a smaller area.

In a short video posted on TMZ, the actor Charlie Sheen invited Dorner to get in touch, noting that he had been praised as "awesome" in the fugitive's rambling, 11,000 word Facebook posting. "You mentioned me in your manifesto, so thank you for your kind words," Sheen said. "I am urging you to call me. Let's figure out together how to end this thing. Call me. I look forward to talking to you."

Dorner has vowed to wage "unconventional and asymmetrical warfare" against his former comrades and has put together a "hit list". On 3 February, Dorner allegedly killed Monica Quan, 28, a basketball coach, and her fiance, Keith Lawrence, 27, as they sat in a car in Irvine, south of LA. Quan was the daughter of a police captain who had represented Dorner – negligently, in Dorner's view – at his tribunal.

After reportedly failing to hijack a boat to Mexico he was spotted near Corona, south of LA, last Thursday. He exchanged shots with a patrol, grazing one officer in the head. About 20 minutes later Dorner reportedly ambushed two officers at a red traffic light in nearby Riverside, killing one, Michael Crane, 34, a veteran, and wounding the other, a trainee. A huge security operation is expected at Crane's funeral on Wednesday.

Controversy has continued to grow over the police shooting last Thursday of a pick-up truck mistaken for Dorner's. Officers fired more than 20 bullets at a 71-year-old mother and daughter who were delivering copies of the LA Times. The mother was hit twice in the back but is expected to recover. The daughter escaped with minor injuries. Police also rammed and shot at another pick-up driven by an airport baggage handler. He was concussed but escaped serious injury. The LAPD has apologised to the victims.